基于靶面温度测量的激光强度时空分布重构方法

基于靶面温度分布测量反演激光强度时空分布的重构表达式中,被积函数包含的奇异阿贝尔核函数导致了求解积分表达式的病态和解的不稳定。为了解决这一积分求解问题,基于广义函数理论和正则变换方法,对积分函数进行了重新构造,获得了基于靶面温度时空分布测量反演入射激光强度分布的重构算法,并分析了重构结果对温度测量误差的敏感性。借助数值模拟方法对重构算法进行了验证,数值计算给出了重构强度误差与靶板厚度和辐照时间的关系。验证结果表明,两种背光面边界条件下反演获得的激光束时空分布,不仅与原始模型激光束达到了较好的一致,而且不受薄板条件的限制。算法对强激光辐照效应的靶面激光参量监测有实用性。

Reconstruction Algorithm for Laser Intensity Temporal-Spatial Distribution from Measured Temperature Distribution on Target Surface

The reconstruction expressions of the laser temporal-spatial distribution retrieved from temperature field of the heated surface have been obtained.Becuase the characteristic Abelian kernel function exists in integral representations,the integrations are ill-conditioned and the solutions are instable.In order to solve the ill-conditioned problems,the generalized functions theory and regular transformation method are utilized to reconstruct the integral functions.The reconstruction algorithm for laser intensity temporal-spatial distribution from measured temperature distribution on the target-surface is obtained.The sensitivity of the retrieved intensities to measured temperature error is analyzed.The developed algorithms is verified by numerical simulation.The relations of reconstructed intensity errors varying wth target thickness and irradiated time are gained by numerical simulation.The results show that the retrieved intensity distributions accord with those in the initial model for two kinds of boundary conditions on the back surface.The algorithm can be applied to monitor laser parameters on the target surface under intense laser irradiation.